The principles of circle geometry are used by navigators at sea. For example, the "horizantal angle of danger" enables a navigator to stay a safe distance from a dangerous region.
The Therom 1- if a tangent and a secant (or a chord) intersect on a circle at the point of tangency, then the measure of the angle formed is one half the measure of its intercepted arc.
Therom 2- the measure of an angle formed by 2 secants or chords that intersect in the interior of a circle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
Therom 3-.the measure of an angle formed by 2 secants that intersec in the exterior of a circle is one half the difference of the measures of the intercepted arcs.
Therom 4- the measure of a secant tangent angle with its vertex outside the circle is one half hte difference of the measures of the intercepted arcs.
Therom 5- the measure of a tangent-tangent angle with the vertex outside the circle is one half the difference of the measures of the intercepted arcs, or the measure of the major arc minus 180 degrees.. 2 tangents
Classifaction of Angles With Circles-
Case 1: Vertex is on circle
Case 2: Vertex is inside the circle
Case 3: Vertex is outside the circle
The Therom 1- if a tangent and a secant (or a chord) intersect on a circle at the point of tangency, then the measure of the angle formed is one half the measure of its intercepted arc.
Therom 2- the measure of an angle formed by 2 secants or chords that intersect in the interior of a circle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
Therom 3-.the measure of an angle formed by 2 secants that intersec in the exterior of a circle is one half the difference of the measures of the intercepted arcs.
Therom 4- the measure of a secant tangent angle with its vertex outside the circle is one half hte difference of the measures of the intercepted arcs.
Therom 5- the measure of a tangent-tangent angle with the vertex outside the circle is one half the difference of the measures of the intercepted arcs, or the measure of the major arc minus 180 degrees.. 2 tangents
Classifaction of Angles With Circles-
Case 1: Vertex is on circle
Case 2: Vertex is inside the circle
Case 3: Vertex is outside the circle